Following his arrest, Peters said he had been suffering a "breakdown".

He said he had been thinking of killing his wife and family for several weeks so they could be "spared the pain and upset when he became bankrupt".

However, inquiries later showed Peters' Kensington-base oriental antiques business was not in trouble and he had money in the bank.

Peters told police he had been visited by a child protection team and feared Sophia would be taken into care.

But an assessment had already concluded on September 27 that he was not a risk to himself or others and the case was closed.

In the months before the killing, Peters searched the internet for "serial killers", "treatment of child killers in prison" and "premeditated murder", the court heard.

He picked the opportunity to kill her before she was due to return to her £5,000-a-term boarding school after the half-term break.

Sophia's mother - Peters' third wife - and other family members sat in court as he admitted murder.

Detective Inspector Helen Rance, of Scotland Yard, said: "Sophia was an innocent seven-year-old girl, much loved by her mother, brother and friends. She was tragically murdered by the hands of her own father in the most frightening way.

"Sophia had her whole life ahead of her, which was taken away so cruelly in an act of pure selfishness. Robert Peters has shown no remorse for the murder, and initially maintained a defence of diminished responsibility. However, due to the strong evidence against him, he has changed his plea to guilty.

"This was a particularly traumatic case to deal with for all concerned, and I hope that this conviction brings a degree of closure to Sophia's family."